Find the differential dy for the given values of x and dx. y=frac{e^x}{10},x=0,dx=0.1

Find the differential dy for the given values of x and dx. y=frac{e^x}{10},x=0,dx=0.1

Question
Differential equations
asked 2020-10-26
Find the differential dy for the given values of x and dx. \(y=\frac{e^x}{10},x=0,dx=0.1\)

Answers (1)

2020-10-27
\(y=e^{\frac{x}{10}}\)
Differentiate both sides with respect to x
\(\frac{dy}{dx}=\frac{d(e^{\frac{x}{10}})}{dx}\)
Using chain rule, we can write
\(\frac{dy}{dx}=\frac{d(e^{\frac{x}{10}})}{d(\frac{x}{10})}\cdot\frac{d(\frac{x}{10})}{dx}\)
Recall: \(\frac{d(e^u)}{du}=e^u\)
\(\frac{dy}{dx}=e^{\frac{x}{10}}\cdot\frac{1}{10}\)
\(\frac{dy}{dx}=\frac{e^{\frac{x}{10}}}{10}\)
Multiply both sides by dx
\(dy=\frac{e^{\frac{x}{10}}}{10dx}\)
Result: \(dy=\frac{e^{\frac{x}{10}}}{10dx}\)
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